Introduction

The event of precipitation is a result of a complex natural process that varies significantly on both temporal and spatial scale (Bohnenstengel et al. 2011). It is one of the most important climatic variables often studied by researchers to understand its changing patterns. The variable nature of precipitation makes it a highly challenging issue for the water resource planners and also agricultural planners. Climate change studies reported an increasing average global temperature trends; however, the average precipitation showed an increasing trend on a global scale while both increasing as well as decreasing trend at local or regional scale (McCarthy 2001). Also, the rise in sea surface temperature (SST) has a significant effect on the increasing rainfall (Trenberth 2011). It is predicted that climate change will affect more adversely the poorer countries. So, the problem of water scarcity as well as food security faced by those very nations will be more pronounced in the future. The agricultural and water sector of the Asia-Pacific region have been already substantially affected by the variable precipitation pattern.

Worldwide, a number studies of precipitation patterns revealed significant decrease in precipitation over Saudi Arabia (Almazroui et al. 2012), Sicily island (Italy) (Cannarozzo et al. 2006), Italy (Buffoni et al. 1999), Kenya (Kipkorir 2002), northeastern part of Brazil (da Silva 2004), Russia (Peterson et al. 2002), and northeast and north China (Zhai and Pan 2003). On the other hand, an increase in precipitation was reported over the Netherlands (Daniels et al. 2014), Changjiang Valley, and the southeastern coast of China (Hu et al. 2003; Zhai and Pan 2003), western coasts of the Philippines (Cruz et al. 2013), New York of USA (Burns et al. 2007), and Mexico (Méndez González et al. 2008).

In India, regional-level studies revealed a significant decreasing trend of precipitation over Madhya Pradesh (Duhan and Pandey 2013; Kundu et al. 2015), Chattisgarh (Meshram et al. 2016), downstream areas of Gomti river basin (Abeysingha et al. 2014), Wainganga Basin (Taxak et al. 2014), while insignificant decrease in rainfall was found over Cauvery river basin (Sushant et al. 2015). However, significant increasing precipitation trend was reported over the Sindh river basin (Madhya Pradesh) (Gajbhiye et al. 2015; Gajbhiye et al. 2016), upstream area of Gomti river basin (Abeysingha et al. 2014), Haryana (Darshana 2012).

Study area

Damodar River originates in the hills of the Chottanagpur Plateau of the Palamau district of Jharkhand (Fig. 1). The Usri, the Barakar, and the Kasai are the tributaries of Damodar River that drains the basin. It is a sub-basin of Ganga basin that lies between 84°35′ to 88°20′ east longitudes and 21°44′ to 24°25′ north latitudes of India. It covers a drainage area of 41,965.49 sq. and have a length of 575 km. It is bounded on the north by Central India hills, in the south and east by the Eastern Ghats, and in the west by Maikala hill range. The climate of the basin characterized by hot and humid summers with moderate winters.

Fig. 1
figure 1

Damodar River Basin area showing grid locations along with DEM

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Data collection

The British Atmospheric Data Center (BADC) is the designated data center that provides global grid datasets of climatic variables. For the present study, CRU TS 3.23 monthly precipitation data at 0.5° × 0.5° grid (1901–2013) was downloaded from Centre of Environmental Data Archival (http://badc.nerc.ac.uk). Eighteen grid points of CRU TS 3.23 dataset cover the whole Damodar basin which is shown in Fig. 1. The annual and monsoon data series was then prepared by adding all the month’s data as annual and monsoon includes precipitations from June–September.

In this study, therefore, an attempt has been made to determine the rainfall climatology over the Damodar River Basin (DRB). The aim of the present study is to identify spatiotemporal variability in precipitation along with the turning point in annual and monsoon season precipitation for a period of 113 years (1901–2013). To analyze spatially the changes in rainfall behavior, the Sen’s slope value of each grid was interpolated using inverse distance weighted (IDW) interpolation in the ArcGIS environment version 10 for the period 1901–2013.

Methodology

Autocorrelation

Autocorrelation is also known as the serial correlation or lagged correlation. It is used to check serial dependence between the data. The lag-1 autocorrelation coefficient is the simple correlation coefficient of the first observations N−1, x t , t = 1,2,3……………..N−1 and the next observations, x t+1 , t = 2, 3, ... N. The first-order correlation coefficient (r1) between x t and x t+1 can be calculated first and then its significance is tested against the null hypothesis following Anderson formula (1941).

If the value of r 1 lie outside the confidence interval (95%), the data are assumed to be serially correlated; otherwise, the sample data are considered to be serially independent.

Mann-Kendall trend test

The Mann-Kendall test is a non-parametric test that was used for the analysis of time series data of rainfall trend in the present study. It is frequently used for the detection of significant trend in hydrologic data series (Patra et al. 2012). The MK test, S statistics for a series X 1, X 2 ………………….X n can be given by

$$ S=\sum_{i=1}^{n-1}\sum_{j=i+1}^n\mathit{\operatorname{sgn}}\left({X}_j-{X}_i\right) $$

where X i is ranked from i = 1, 2 … n − 1 and X j ranked from j = i + 1, 2, and n is the length of thedataset.

$$ Sgn\left(\vartheta \right)=\left\{\begin{array}{c}1\dots . if\ \vartheta >0\\ {}0\dots if\ \vartheta =0\\ {}-1\dots . if\ \vartheta <0\end{array}\right. $$

The value of S whether negative or positive displays either increasing or decreasing trend. For the sample size n ≥ 8, variance of the Mann-Kendall statistics is given by

$$ Var(S)=\frac{\left[n\left(n-1\right)\left(2n+1\right)-\sum_tt\left(t-1\right)\left(2t+5\right)\right]}{18} $$

where t i is the number of ties present up to sample i.

The standardized MK test statistics (Z mk ) can be estimated by the following given formula:

$$ {Z}_{mk}=\left\{\begin{array}{c}\frac{S-1}{\sqrt{V(S)}}\kern1em if\ S>0\\ {}0\kern2.75em if\ S=0\\ {}\frac{S+1}{\sqrt{V(S)}}\kern0.75em if\ S<0\end{array}\right. $$

The Z mk follows a standard normal distribution and if its value is positive, it signifies an upward trend and if negative, it signifies a decreasing trend. If the value of Z mk is greater than Z ά/2 , it is considered as significant trend (where ά is significance level) and the null hypothesis is rejected.

Theil-Sen’s slope method

In addition to trend identification, the magnitude of the drift was also computed by the Sen’s slope (β) method, which was suggested by Sen (1968). This is a non-parametric method (Sen, 1968) by which slope of N pairs of data points is estimated. It quantifies the linear median (50th percentile) concentration changes with time and is used to determine the magnitude of the trend line. A positive value of Sen’s slope indicates an “upward (increasing) trend” and a negative value suggests a “downward (decreasing) trend” in the time series.

Modified Mann-Kendall

Modified Mann-Kendall (MMK) has been applied to detect trend in serially correlated data. In this method, the significant values of ρk (autocorrelation coefficient) are used to estimate variance correction factor\( \raisebox{1ex}{$n$}\!\left/ \!\raisebox{-1ex}{${n}_s^{\ast }$}\right. \), as the variance of S is undervalued when data are positively auto-correlated.

$$ \frac{n}{n_s^{\ast }}=1+\frac{2}{n\left(n-1\right)\left(n-2\right)}\times \sum_{K=1}^{n-1}\left(n-k\right)\left(n-k-1\right){\left(n-k-2\right)}_{\rho k} $$

The revised variance is calculated by the given formula:

$$ {V}^{\ast }(S)=V(S)\times \frac{n}{n_s^{\ast }} $$

where V(S) is the same as it was computed in the Mann-Kendall method.

Sequential Mann-Kendall

Sneyres (1990) introduced the sequential Mann-Kendall test to detect abrupt potential turning points in long-term data. This test involves the computation of two series: one is progressive and another one is retrogressive. When the two series cross each other and deviate beyond the confidence limit of 95%, then that point will be a statistically significant turning point. It is computed by comparing the values of xj annual mean time series (j = 1,...,n) with xi, (i = 1,...,j − 1) (Nasri and Modarres 2009). At the time of comparison, the cases where xj > xi is counted and denoted by nj.

Then, test statistic t is computed by using following equation:

$$ {t}_{j=}\sum_1^j{n}_j $$

The mean and variance of the test statistic are

$$ E(t)=\frac{n\left(n-1\right)}{4} $$

and

$$ Var\left({t}_j\right)=\left[j\left(j-1\right)\left(2j+5\right)\right]/72 $$

The sequential values of the statistic u(t) are then calculated as

$$ u(t)=\frac{t_j-E(t)}{\sqrt{Var\left({t}_j\right)}} $$

The values of u′(t) retrogressive series are computed similarly, but starting from end of the series.

Results and discussion

In the present paper, rainfall trend analysis has been done in order to study the variability of rainfall over the basin. This is the first attempt to give a full picture of the spatial and temporal rainfall trend analysis covering Damodar basin. Damodar River basin covers a variety of topographic features like in the northwest; it covers the plateau region while on the southeast region, it is bounded by sea. These different topographic features result into different climatic conditions over the basin. Thus, the understanding of rainfall variability is essential for water resource management, proper agricultural activities so that accurate valuation of supplementary water requirements can be done.

Lag-1 autocorrelation at 1, 5, and 10% significance level was applied to both the annual and monsoon season data whose results are shown in Table 1. Results of autocorrelation found the presence of lag-1 autocorrelation in Grid 1, Grid 2, Grid 3, Grid 4, Grid 13, Grid 14 and Grid 16 for annual series and during the monsoon season in Grid 1, Grid 2, Grid 3, Grid 4, Grid 5, Grid 6, and Grid 16. The Modified Mann-Kendall test (Hamed and Rao 1998) was applied to the serially correlated data and for the rest data, Mann-Kendall trend test (Mann 1945) applied (Table 1).

Table 1 Trend analysis (Mann-Kendall z statistics and Sen’s slope (Q) value) and percent change of annual and seasonal precipitation (1901–2013)
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MK statistics results indicated a significant decreasing trend annually at almost all the grid points (at 1, 5, and 10% significance level) except grids 14, 16, 17, and 18 which showed an insignificant increasing trend. The amount of the decreasing trends in annual precipitation ranged between 0.56 mm per year (Grid 13) and 2.43 mm per year (Grid 2) while, the increasing trends in annual rainfall ranged between 0.32 mm per year (Grid 14) and 1.78 mm per year (Grid 2). This shows a decline in rainfall in the northwestern region of the basin while an increment in rainfall over the southeastern region. The southeastern region of basin is near to sea coast and influence of sea may be responsible for insignificant rise of rainfall in that region. The spatial distribution of trend magnitude (mm/year) for annual rainfall is shown in Fig. 2. The Mann-Kendall test revealed a negative trend in annual rainfall, but it does not count for the identification of shift point. Hence, sequential Mann-Kendall test was applied to see if there were any abrupt changes.

Fig. 2
figure 2

Spatial distribution of Sen’s slope value (mm/year) for the annual rainfall

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The results of sequential Mann-Kendall indicating significant and first turning point were displayed for both annual and monsoon season data in Table 2. Results of sequential Mann Kendall (Fig. 3) showed declining trend in almost all the grid points for annual rainfall except for grid 14, 16, 17, and 18 which showed a periodic fluctuation with an increasing trend .

Table 2 Significant change points by sequential Mann-Kendall test over Damodar basin
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Fig. 3
figure 3figure 3

Sequential Mann-Kendall test rank statistics for annual rainfall over all the grid locations

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In India, monsoon is associated with El Niño Southern Oscillation (ENSO). During El Niño, weaker monsoon prevails in India as it causes suppression of the trade winds which are responsible for bringing monsoon. Krishnamurthy and Goswami (2000) observed that the inter-decadal decrease in monsoon rainfall occurred due to the El Niño. Another possible cause of the decreasing monsoon rainfall trend may be the rapid warming in the Indian Ocean. Warming of Indian Ocean potentially weakens the land-sea thermal difference that reduces the rainfall over parts of South Asia (Roxy et al. 2015). Stephenson and Kumar (2001) found weakening of the monsoon circulation using results from the recent atmospheric general circulation experiments for Asian summer monsoon. The conclusion drawn from a number of studies has also indicated decreasing rainfall in Asia (Dash et al. 2007; Goswami et al. 2006; Khan et al. 2000; Lal 2003; Min et al. 2003; Mirza 2002; Shrestha et al. 2000; Sinha Ray and Srivastava 1999). Many researchers found decrease in South Asian monsoon rainfall (Loo et al. 2015; Roxy et al. 2015; Schewe and Levermann 2012; Sinha et al. 2015). Plausible explanation of the reduction in rainfall over South Asia has been given by Roxy et al. (2015) who reported that increased SST over Indian Ocean potentially weakens the land-sea thermal difference that reduces the rainfall over parts of South Asia.

It can be seen from the results that for most of the grid points, the significant turning point was found in between 1940 and 1950. Grids 17 and 18 showed an increasing trend as depicted from u(t) statistics. The u(t) statistics displayed an upward change after 1909 till present in grid 18. Successive increasing and decreasing trend was found for grids 14, 15, and 16.

From Fig. 2, it can be concluded that for Grid 1, two significant turning points were clearly identified, i.e., 1944 and 2000. Grid 2 also showed two significant turning points that are 1997 and 1949. On the other hand, Grid 11 showed three significant turning points that are 1916, 1919, and 1943. 1944 was the most important turning point in the study as it was found significant for grids 1, 8, 9, and 10. No turning point was found for grids 13, 14, 15, 16, and 17.

The results of MK and MMK showed a significant decreasing trend for monsoon rainfall for all the grids except grids 14, 16, 17, and 18. Positive trend were not significant except for grid 18.The amount of the decreasing trends in monsoon precipitation ranged between 0.54 mm per year (grid 15) and 2.26 mm per year (grid 4). However, the increasing trends in rainfall during monsoon ranged between 0.05 mm per year (grid 16) and 1.16 mm per year (grid 18) (Fig. 4).

Fig. 4
figure 4

Spatial distribution of Sen’s slope value (mm/year) for the annual rainfall

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The u(t) statistics depicted a decreasing trend of monsoon rainfall for grid 1 to grid 15 (Fig. 5). High periodic fluctuations in monsoon rainfall were found for grids 14 and 16. For grid 17 and grid 18, an increasing trend in monsoon rainfall was observed. No turning point was found for grids 11, 13, 14, 15, 16, 17, and 18. It can be seen from the results that for most of the grid points, the significant turning point was found in between 1940 and 1950 and 1990 and 2000.

Fig. 5
figure 5figure 5

Sequential Mann-Kendall test rank statistics for monsoon rainfall over the all the grid locations

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Results of trend analysis showed a declining as well as episodic fluctuation of rainfall trend in most of the cases. The declining trend in rainfall is in agreement with other studies who also found decrement in annual as well as monsoon rainfall over the Wainganga basin (Taxak et al. 2014 ), Sindh river basin (Gajbhiye et al. 2016), Chhattisgarh (Meshram et al. 2016), Yamuna River basin (Rai et al. 2010), Seonath River basin (Chakraborty et al. 2013), and Madhya Pradesh (Duhan and Pandey 2013; Kundu et al. 2015) which are in different parts of India. However, the present study is in contradiction with the results of trend analysis found over Haryana (Darshana 2012), Haridwar (Pranuthi et al. 2014), Gangetic West Bengal, western Uttar Pradesh, Jammu and Kashmir, Konkan and Goa, Madhya Maharashtra, Rayalaseema, coastal Andhra Pradesh, and north Interior Karnataka (Guhathakurta and Rajeevan 2008) which showed the increasing precipitation trend.

Percent change was also computed for both annual and monsoon season rainfall data. For annual precipitation, the percentage change found more than 10% in 11 grids while for monsoon season, it was found more than 10% in 13 grids. The maximum negative percent change was found at grid 2 (−23.39) while minimum at grid 13 (−4.39) for annual series. Also, for monsoon season, the maximum negative percent change was found at grid 2 (−24) while minimum at grid 13 (−0.60).

The results showed temporal variability in rainfall trend which shows that the location, topography, altitude, and regional climate along with climate change have a complex relationship which results into these contradictory outcomes from one location to another location.

The most probable causes associated with the fluctuation in rainfall include the following reasons.

  • Weakening of the global monsoon circulation (Duan and Yao 2003)

  • Reduction in strength of tropical easterly Jet Stream, which are important for the formation of monsoon depression (Naidu et al. 2011; Rao et al. 2004; Sathiyamoorthy 2005)

  • Rise in global temperature as a result of global warming leads to an uneven distribution of rainfall (Rao et al. 2001).

  • Reduction in forest cover (Gupta et al. 2005; Nair et al. 2003)

  • Rising aerosol content due to anthropogenic activities (Ramanathan et al. 2005; Sarkar and Kafatos 2004)

Increased temperature has direct influence on moisture holding capacity of air as it is positively correlated with it; hence, it may result in more extreme and intense rainfall with a decrease in rainy days keeping rainfall stable during the considered time span (Trenberth 1998). Kumar et al. (1987) also reported that the warming in the Indian temperature mainly resulted from increasing temperatures up to the late 1950s, after which temperature remained nearly stable over India.

Conclusion

The present study involves the analysis of annual and monsoon rainfall trend for the entire Damodar basin over the period 1901–2013, covering 18 grid points. The significant decreasing trend in precipitation were found over the basin annually as well as for monsoon season for most of the grid locations. In the annual series, the decline in magnitude of trend varies from 0.56 mm per year (grid 13) to 2.43 mm per year (grid 2). During monsoon season rainfall, the magnitude of the declining trend varies from 0.54 mm per year (grid 15) to 2.26 mm per year (grid 4).

The results of sequential Mann-Kendall test revealed the decreasing trend with periodic fluctuations in almost all the grid points for both annual and monsoon series. The results of the present study revealed that the declining trend of rainfall can have impacts on water resources and agriculture of the area. So, the water policy makers and agriculture planners have to adapt water conservation strategies along with this agriculture practitioners moving to crops or breeds requiring less water.

From the study, it is concluded that annual and monsoon precipitation is decreased significantly in DRB during the period 1901–2013. The decreasing trend in seasonal rainfall will have a more pronounced effect on agricultural activities that may affect the growth phase of the kharif crops (May–October) in the basin. There is a need to integrate the changing climate in the planning and management of water resources of the state. As the Damodar basin covers some areas of Jharkhand, where the agriculture is totally dependent on rainfall, the agriculture planners should actively incorporate some strategies to avoid the water stress condition.

On the basis of the results found in the present study, the future scope including the study of land use cover changes, temperature trends along with population and aerosol trends will be helpful in determining the probable reasons of decrement of rainfall.